Method and apparatus for estimating channel in communication system

ABSTRACT

A method of estimating a channel of a base station in a communication system using an IRS may comprise: receiving a first signal through a direct path between a terminal and the base station from the terminal and a second signal through an indirect path through the IRS from the terminal; estimating a first angle of arrival of the second signal received from the IRS; estimating a second angle of arrival of a signal transmitted to the IRS by the terminal based on the estimated first angle of arrival; estimating a third angle of arrival of the first signal received from the terminal based on the estimated first angle of arrival; and estimating path gains on the direct path and the indirect path based on the estimated first angle of arrival to the estimated third angle of arrival.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to Korean Patent Application No.10-2021-0188969, filed on Dec. 27, 2021 with the Korean IntellectualProperty Office (KIPO), the entire contents of which are herebyincorporated by reference.

BACKGROUND 1. Technical Field

Example embodiments of the present disclosure relate to an intelligentreflecting surface technology in a communication system, and moreparticularly, to a technology for estimating a channel in acommunication system using an intelligent reflecting surface.

2. Related Art

A communication system using an intelligent reflecting surface (IRS) mayinclude low-cost passive elements which reflect an incident signal andmay control a reflection pattern of the passive elements to form anadvantageous propagation channel. Even when a direct path between a basestation and a terminal is blocked, a communication system using anintelligent reflecting surface can generate an additional indirect path,which can compensate for disadvantages of millimeter wave bandcommunication, such as high straightness and large path loss.

However, in order to realize potential advantages of a communicationsystem using an intelligent reflecting surface, a base station needs toacquire accurate channel state information of a direct path between thebase station and a terminal and an indirect path between the basestation, the intelligent reflecting surface, and the terminal. However,due to a non-linear relationship between millimeter wave channelparameters composed of a reflection pattern of an intelligent reflectingsurface, an angle of departure of a received signal, an angle ofarrival, and a path gain, it may be difficult for a base station toestimate accurate channel state information.

As a method of estimating a channel, there may be a method in which abase station may completely turn elements of an intelligent reflectingsurface off to estimate a direct channel between the base station and aterminal and then may turn the intelligent reflecting surface on tosubtract an influence of a direct channel from a received signal usingdirect channel information estimated first and then estimate an indirectchannel. However, there may be a problem in that an error of the firstestimated direct channel information affects the performance ofsubsequent indirect channel estimation.

According to another method of estimating a channel, that is, a methodin which a base station estimates a direct path channel and an indirectpath channel together, it is possible to solve a problem in whichestimation affects mutual performance, but there may be a problem inthat channel state information between the base station and anintelligent reflecting surface should be known in advance.

SUMMARY

Accordingly, example embodiments of the present disclosure are providedto substantially obviate one or more problems due to limitations anddisadvantages of the related art.

Example embodiments of the present disclosure provide a method and anapparatus for reducing computational complexity of complex channelestimation and improving performance in an intelligent reflectingsurface-based communication system.

According to a first exemplary embodiment of the present disclosure, amethod of estimating a channel of a base station in a communicationsystem using an intelligent reflecting surface may comprise: receiving afirst signal through a direct path between a terminal and the basestation from the terminal and a second signal through an indirect paththrough the intelligent reflecting surface from the terminal; estimatinga first angle of arrival of the second signal received from theintelligent reflecting surface; estimating a second angle of arrival ofa signal transmitted to the intelligent reflecting surface by theterminal based on the estimated first angle of arrival; estimating athird angle of arrival of the first signal received from the terminalbased on the estimated first angle of arrival; and estimating path gainson the direct path and the indirect path based on the estimated firstangle of arrival to the estimated third angle of arrival.

The receiving of the first signal through the direct path between theterminal and the base station from the terminal and the second signalthrough the indirect path through the intelligent reflecting surfacefrom the terminal may further include, when a third signal in which thefirst signal and the second signal are added is received from theterminal, separating the first signal and the second signal from thethird signal.

The first angle of arrival may be estimated based on a first algorithm;and the first algorithm may include at least one of a root-multiplesignal classification (root-MUSIC) algorithm and a semi-definiteprogramming algorithm.

The second angle of arrival may be estimated by iteratively applying anarray response vector in which all elements are 1 and a maximumlikelihood estimation method in a time domain.

The third angle of arrival may be estimated by iteratively applying amaximum likelihood estimation method.

The path gain on the direct path and the path gain on the indirect pathmay be estimated based on a linear estimation method using the estimatedfirst angle of arrival to the estimated third angle of arrival.

An on-off reflection pattern of the intelligent reflecting surface maybe varied according to a type of an antenna array included in the basestation.

The on-off reflection pattern may be determined based on the number ofreflection repetitions.

When the base station includes a planar array antenna, the on-offreflection pattern may include a reflection element shared when thenumber of reflection repetitions in a horizontal direction and thenumber of reflection repetitions in a vertical direction are eachmaximum.

The intelligent reflecting surface may include a plurality ofdynamically adjustable reflectors; and a communication channel betweenthe intelligent reflecting surface and the base station may be a channelin which one line-of-sight propagation path is present.

According to a second exemplary embodiment of the present disclosure, abase station in a communication system using an intelligent reflectingsurface may comprise: a processor; a memory configured to electronicallycommunicate with the processor; and instructions stored in the memory,wherein, when the instructions are executed by the processor, theinstructions operate to cause the base station to: receive a firstsignal through a direct path between a terminal and the base stationfrom the terminal and a second signal through an indirect path throughthe intelligent reflecting surface from the terminal; estimate a firstangle of arrival of the second signal received from the intelligentreflecting surface; estimate a second angle of arrival of a signaltransmitted to the intelligent reflecting surface by the terminal basedon the estimated first angle of arrival; estimate a third angle ofarrival of the first signal received from the terminal based on theestimated first angle of arrival; and estimate path gains on the directpath and the indirect path based on the estimated first angle of arrivalto the estimated third angle of arrival.

When the first signal through the direct path between the terminal andthe base station and the second signal through the indirect path throughthe intelligent reflecting surface are received from the terminal, theinstructions may operate to cause the base station to, when a thirdsignal in which the first signal and the second signal are added isreceived from the terminal, separate the first signal and the thirdsignal from the third signal.

The instructions may operate to cause the base station to estimate thefirst angle of arrival based on a first algorithm; and the firstalgorithm may include at least one of a root-multiple signalclassification algorithm and a semi-definite programming algorithm.

The instructions may operate to cause the base station to estimate thesecond angle of arrival by iteratively applying an array response vectorin which all elements are 1 and a maximum likelihood estimation methodin a time domain.

The instructions may operate to cause the base station to estimate thethird angle of arrival by iteratively applying a maximum likelihoodestimation method.

The instructions may operate to cause the base station to estimate thepath gain on the direct path and the path gain on the indirect pathbased on a linear estimation method using the estimated first angle ofarrival to the estimated third angle of arrival.

The instructions may operate to cause the base station to vary an on-offreflection pattern of the intelligent reflecting surface according to atype of an antenna array included in the base station.

The instructions may operate to cause the base station to determine theon-off reflection pattern based on the number of reflection repetitions.

When the base station includes a planar array antenna, the instructionsmay operate to cause the on-off reflection pattern to include areflection element shared when the number of reflection repetitions in ahorizontal direction and the number of reflection repetitions in avertical direction are each maximum.

According to the present disclosure, in an IRS-based communicationsystem, direct and indirect channels can be simultaneously estimatedwithout prior knowledge of channel state information. In addition, in anIRS-based communication system, training overhead can be reduced usingantenna structure information. Accordingly, the performance of amillimeter wave band communication system can be improved.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a conceptual diagram illustrating an exemplary embodiment of acommunication system.

FIG. 2 is a block diagram illustrating an exemplary embodiment of acommunication node constituting a communication system.

FIG. 3 is a conceptual diagram illustrating a communication system modelusing an IRS.

FIG. 4 is a block diagram illustrating a method of estimating a channelthrough two operations in a communication system using an IRS.

FIG. 5 is a flowchart illustrating the first operation of the method ofestimating a channel.

FIG. 6 is a flowchart illustrating the second operation of the method ofestimating a channel.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Since the present disclosure may be variously modified and have severalforms, specific exemplary embodiments will be shown in the accompanyingdrawings and be described in detail in the detailed description. Itshould be understood, however, that it is not intended to limit thepresent disclosure to the specific exemplary embodiments but, on thecontrary, the present disclosure is to cover all modifications andalternatives falling within the spirit and scope of the presentdisclosure.

Relational terms such as first, second, and the like may be used fordescribing various elements, but the elements should not be limited bythe terms. These terms are only used to distinguish one element fromanother. For example, a first component may be named a second componentwithout departing from the scope of the present disclosure, and thesecond component may also be similarly named the first component. Theterm “and/or” means any one or a combination of a plurality of relatedand described items.

In exemplary embodiments of the present disclosure, “at least one of Aand B” may refer to “at least one of A or B” or “at least one ofcombinations of one or more of A and B”. In addition, “one or more of Aand B” may refer to “one or more of A or B” or “one or more ofcombinations of one or more of A and B”.

When it is mentioned that a certain component is “coupled with” or“connected with” another component, it should be understood that thecertain component is directly “coupled with” or “connected with” to theother component or a further component may be disposed therebetween. Incontrast, when it is mentioned that a certain component is “directlycoupled with” or “directly connected with” another component, it will beunderstood that a further component is not disposed therebetween.

The terms used in the present disclosure are only used to describespecific exemplary embodiments, and are not intended to limit thepresent disclosure. The singular expression includes the pluralexpression unless the context clearly dictates otherwise. In the presentdisclosure, terms such as ‘comprise’ or ‘have’ are intended to designatethat a feature, number, step, operation, component, part, or combinationthereof described in the specification exists, but it should beunderstood that the terms do not preclude existence or addition of oneor more features, numbers, steps, operations, components, parts, orcombinations thereof.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this disclosure belongs. Termsthat are generally used and have been in dictionaries should beconstrued as having meanings matched with contextual meanings in theart. In this description, unless defined clearly, terms are notnecessarily construed as having formal meanings.

Hereinafter, forms of the present disclosure will be described in detailwith reference to the accompanying drawings. In describing thedisclosure, to facilitate the entire understanding of the disclosure,like numbers refer to like elements throughout the description of thefigures and the repetitive description thereof will be omitted.

A communication system to which exemplary embodiments according to thepresent disclosure are applied will be described. The communicationsystem to which the exemplary embodiments according to the presentdisclosure are applied is not limited to the contents described below,and the exemplary embodiments according to the present disclosure may beapplied to various communication systems. Here, the communication systemmay have the same meaning as a communication network.

FIG. 1 is a conceptual diagram illustrating an exemplary embodiment of acommunication system.

Referring to FIG. 1 , a communication system 100 may comprise aplurality of communication nodes 110-1, 110-2, 110-3, 120-1, 120-2,130-1, 130-2, 130-3, 130-4, 130-5, and 130-6. The plurality ofcommunication nodes may support 4^(th) generation (4G) communication(e.g., long term evolution (LTE), LTE-advanced (LTE-A)), 5^(th)generation (5G) communication (e.g., new radio (NR)), or the like. The4G communication may be performed in a frequency band of 6 GHz or below,and the 5G communication may be performed in a frequency band of 6 GHzor above.

For example, for the 4G and 5G communications, the plurality ofcommunication nodes may support a code division multiple access (CDMA)based communication protocol, a wideband CDMA (WCDMA) basedcommunication protocol, a time division multiple access (TDMA) basedcommunication protocol, a frequency division multiple access (FDMA)based communication protocol, an orthogonal frequency divisionmultiplexing (OFDM) based communication protocol, a filtered OFDM basedcommunication protocol, a cyclic prefix OFDM (CP-OFDM) basedcommunication protocol, a discrete Fourier transform spread OFDM(DFT-s-OFDM) based communication protocol, an orthogonal frequencydivision multiple access (OFDMA) based communication protocol, a singlecarrier FDMA (SC-FDMA) based communication protocol, a non-orthogonalmultiple access (NOMA) based communication protocol, a generalizedfrequency division multiplexing (GFDM) based communication protocol, afilter bank multi-carrier (FBMC) based communication protocol, auniversal filtered multi-carrier (UFMC) based communication protocol, aspace division multiple access (SDMA) based communication protocol, orthe like.

In addition, the communication system 100 may further include a corenetwork. When the communication system 100 supports the 4Gcommunication, the core network may comprise a serving gateway (S-GW), apacket data network (PDN) gateway (P-GW), a mobility management entity(MME), and the like. When the communication system 100 supports the 5Gcommunication, the core network may comprise a user plane function(UPF), a session management function (SMF), an access and mobilitymanagement function (AMF), and the like.

Meanwhile, each of the plurality of communication nodes 110-1, 110-2,110-3, 120-1, 120-2, 130-1, 130-2, 130-3, 130- 4, 130-5, and 130-6constituting the communication system 100 may have the followingstructure.

FIG. 2 is a block diagram illustrating an exemplary embodiment of acommunication node constituting a communication system.

Referring to FIG. 2 , a communication node 200 may comprise at least oneprocessor 210, a memory 220, and a transceiver 230 connected to thenetwork for performing communications. Also, the communication node 200may further comprise an input interface device 240, an output interfacedevice 250, a storage device 260, and the like. The respectivecomponents included in the communication node 200 may communicate witheach other as connected through a bus 270.

However, each component included in the communication node 200 may beconnected to the processor 210 via an individual interface or a separatebus, rather than the common bus 270. For example, the processor 210 maybe connected to at least one of the memory 220, the transceiver 230, theinput interface device 240, the output interface device 250, and thestorage device 260 via a dedicated interface.

The processor 210 may execute a program stored in at least one of thememory 220 and the storage device 260. The processor 210 may refer to acentral processing unit (CPU), a graphics processing unit (GPU), or adedicated processor on which methods in accordance with embodiments ofthe present disclosure are performed. Each of the memory 220 and thestorage device 260 may be constituted by at least one of a volatilestorage medium and a non-volatile storage medium. For example, thememory 220 may comprise at least one of read-only memory (ROM) andrandom access memory (RAM).

Referring again to FIG. 1 , the communication system 100 may comprise aplurality of base stations 110-1, 110-2, 110-3, 120-1, and 120-2, and aplurality of terminals 130-1, 130-2, 130-3, 130-4, 130-5, and 130-6. Thecommunication system 100 including the base stations 110-1, 110-2,110-3, 120-1, and 120-2 and the terminals 130-1, 130-2, 130-3, 130-4,130-5, and 130-6 may be referred to as an ‘access network’. Each of thefirst base station 110-1, the second base station 110-2, and the thirdbase station 110-3 may form a macro cell, and each of the fourth basestation 120-1 and the fifth base station 120-2 may form a small cell.The fourth base station 120-1, the third terminal 130-3, and the fourthterminal 130-4 may belong to cell coverage of the first base station110-1. Also, the second terminal 130-2, the fourth terminal 130-4, andthe fifth terminal 130-5 may belong to cell coverage of the second basestation 110-2. Also, the fifth base station 120-2, the fourth terminal130-4, the fifth terminal 130-5, and the sixth terminal 130-6 may belongto cell coverage of the third base station 110-3. Also, the firstterminal 130-1 may belong to cell coverage of the fourth base station120-1, and the sixth terminal 130-6 may belong to cell coverage of thefifth base station 120-2.

Here, each of the plurality of base stations 110-1, 110-2, 110-3, 120-1,and 120-2 may refer to a Node-B, evolved Node-B (eNB), base transceiverstation (BTS), radio base station, radio transceiver, access point,access node, road side unit (RSU), radio remote head (RRH), transmissionpoint (TP), transmission and reception point (TRP), eNB, gNB, or thelike. Here, each of the plurality of terminals 130-1, 130-2, 130-3,130-4, 130-5, and 130-6 may refer to a user equipment (UE), terminal,access terminal, mobile terminal, station, subscriber station, mobilestation, portable subscriber station, node, device, Internet of things(IoT) device, mounted apparatus (e.g., a mounted module/device/terminalor an on-board device/terminal, etc.), or the like.

Hereinafter, a communication system using an intelligent reflectingsurface (IRS) will be described. When a method (e.g., signaltransmission or reception) performed by a first communication node(transmission node) among communication nodes is described, a secondcommunication node (or reception node) that corresponds to the firstcommunication node may also perform a method (e.g., signal reception ortransmission) corresponding to the method performed by the first node.That is, when an operation of a terminal is described, a base stationcorresponding to the terminal may perform an operation that correspondsto the operation of the terminal. On the other hand, when an operationof a base station is described, a terminal corresponding to the basestation may perform an operation that corresponds to the operation ofthe terminal.

IRS-based Communication System Model

FIG. 3 is a conceptual diagram illustrating a communication system modelusing an IRS.

Referring to FIG. 3 , a millimeter wave communication system using anIRS may include U terminals including a single antenna, a base stationin which M half-wavelength interval linear array antennas are installed,and an IRS including N dynamically adjustable reflectors. In uplinkcommunication in which each terminal transmits a signal to the basestation, the terminal may continuously transmit a training pilot symboland a data symbol to the base station at a predetermined time interval.A training period may be divided into a total of U time intervals, andeach time interval may include K pilot symbols. Therefore, each terminalmay transmit a signal to the base station at an individual time intervalto avoid interference between terminals. A training symbol y_(k,u) thatis received k-th symbol time (k ∈ {1, ...,K}) by the base station from au-th terminal (u ∈ {1, ..., U}) may be calculated as in Equation 1below.

y_(k, u) = (h_(u) + Fdiag(w_(k))g_(u))x_(k, u) + n_(k, u)

In Equation 1, h_(u) ∈ ℂ^(M) may denote a channel between the basestation and the terminal, g_(u) ∈ ℂ^(N) may denote a channel between theIRS and the terminal, and F ∈ ℂ^(M×N) may denote a channel between thebase station and the IRS. w_(k) ∈ ℂ^(N) may denote a reflection patternof the IRS at a k time. n_(ku)~CN(0_(M), σ²I_(M)) may denote additivewhite noise with a mean of 0 and a variance of σ². x_(k,u) may denote apilot signal transmitted to the base station by the u-th terminal at thek time and in the following example embodiments, for simplicity ofexpression, it may be assumed that

$\left| x_{k,u} \right| = \sqrt{\rho}.$

Assuming that the IRS is installed at a high position on a roof of abuilding or the like, the channel between the base station and the IRSmay be expressed as a channel in which only one line-of-sightpropagation path is present. Based on a geometrical channel model, amillimeter wave band channel between the base station and the IRS can beexpressed as F =

α_(f)u_(M)(υ_(f))u_(N)^(H)(ξ_(f)).

α_(ƒ) may denote a channel gain, ψ_(ƒ) may denote an angle of arrival ofa signal, and ξ_(ƒ) may denote an angle of departure. u_(M)(ϑ) maydenote a steering vector of the M linear array antennas and may becalculated as in Equation 2 below.

u_(M)(ϑ) = [1, e^(jπϑ), ⋯, e^(jπϑ(M − 1))]^(T)for ϑ ∈ (−1, 1)

In Equation 2, ϑ may denote a normalized angle and may satisfy arelationship of ϑ = cos(ϑ) with a physical angle ϑ ∈ (0, π).

The terminal may be positioned at a relatively low altitude. Therefore,the channel between the IRS and the terminal and the channel between thebase station and the terminal may be expressed as

$\text{g}_{u} = {\sum_{\mathcal{l} = 1}^{L_{g}}{\text{α}_{g,\mathcal{l},u}\text{u}_{N}\left( \xi_{g,\mathcal{l},u} \right)\text{and h}_{u} = {\sum_{\mathcal{l} = 1}^{L_{h}}{\beta_{\mathcal{l},u}\text{u}_{M}}}\left( \varphi_{\mathcal{l},u} \right),}}$

respectively. L_(g) and L_(h) may denote the number of paths present ineach channel, α_(g,ℓ,u) may denote a channel gain between the IRS andthe u-th terminal, and ξ_(g,ℓ,u) may denote an angle of arrival of asignal between the IRS and the u-th terminal. β_(ℓ,u) may denote achannel gain between the base station and the u-th terminal, and φ_(ℓ,u)may denote an angle of arrival of a signal between the base station andthe u-th terminal.

When the base station receives K pilot reception signal vectors from theu-th terminal, a reception signal matrix

Y_(u) = [y_(1, u,) ⋅ ⋅⋅, y_(K, u)] ∈ ℂ^(M × K)

may be calculated as in Equation 3 below.

$\begin{matrix}{\text{Y}_{u} = \sqrt{\rho}\left( {\text{h}_{u}1_{K}^{T} + \text{Fdiag}\left( \text{g}_{u} \right)\text{W}} \right) + \text{N}_{u}} \\{= \sqrt{\rho}{\sum\limits_{\mathcal{l} = 1}^{L_{h}}{\beta_{\mathcal{l},u}\text{u}_{M}\left( \varphi_{\mathcal{l},u} \right)1_{K}^{T} + \sqrt{\rho}\text{u}_{M}\left( \upsilon_{f} \right){\sum\limits_{\mathcal{l} = 1}^{L_{g}}{\alpha_{\mathcal{l},u}\text{u}_{N}^{H}\left( \xi_{\mathcal{l},u} \right)\text{W+N}_{u}}}}}}\end{matrix}$

In Equation 3,

W=[w₁, ⋅ ⋅ ⋅, w_(k)]and N_(u) = [n_(1, u), ⋅ ⋅ ⋅, n_(k, u)]

may be matrices representing a reflection pattern and a noise of theIRS, respectively. In Equation 3, a dependent path gain between the basestation, the IRS, and the u-th terminal may be defined as α_(ℓ,u)α_(ƒ)α_(g,ℓ,u), and a dependent path angle between the base station, theIRS, and the u-th terminal may be defined as ξ_(ℓ,u) ξ_(ƒ) - ξ_(g,ℓ,u·)In a communication system in a millimeter wave environment of thepresent example embodiments, since it may be assumed that both a directpath between the base station and the terminal and a dependent indirectpath using the IRS are sparse in an angular space, a length K of a pilotsignal can be set as max(L_(g), L_(h)) < K ≤ N.

Proposed Method of Estimating Channel Through Two Operations

FIG. 4 is a block diagram illustrating a method of estimating a channelthrough two operations in a communication system using an IRS.

Referring to FIG. 4 , in the communication system model using theabove-described IRS, in order to estimate a channel according to thepresent example embodiments, it may be important for the base station toestimate angles ψ_(ƒ),

ξ_(u) = [ξ_(1, u), ⋅ ⋅ ⋅, ξ_(Lg, u)]^(T), andφ_(u) = [φ_(1, u), ⋅ ⋅ ⋅, φ_(Lh, u)]^(T)

on a path. In the method of estimating a channel, a method in which thebase station estimates an angle on a path may include the firstoperation S401 of estimating φ_(ƒ) through a root-multiple signalclassification (root-MUSIC) algorithm and the second operation S402 andS403 of estimating ξ_(u) and φ_(u) based on the estimated φ_(ƒ) throughan iterative maximum likelihood estimation method. After the basestation estimates all angles on the path, the base station may obtainpath gains α_(u) = [α_(1,u), ···, α_(Lg,u) ]^(T) and β_(u) = [β_(1,u),··· , β_(Lh,u)] ^(T) through a linear estimation method.

The base station may receive each of a signal through a direct path anda signal through an indirect path from the terminal. Alternatively, thebase station may receive a signal, in which the signal through thedirect path and the signal through the indirect path are added, from theterminal. Accordingly, the base station may estimate an angle and a pathgain on each path by separating the signal through the direct path andthe signal through the indirect path from the received signal in whichthe signal through the direct path and the signal through the indirectpath are added. The base station may use channel sparsity of amillimeter wave band and an antenna manifold structure to estimate theangle and path gain on the path. Therefore, the base station may use anon-off reflection pattern of the IRS as in Equation 4 below.

$\text{W=}\begin{bmatrix}\text{I}_{K} \\{0_{N - K}0_{K}^{T}}\end{bmatrix}$

A reception signal matrix when the base station receives K pilotreception signal vectors from the u-th terminal using the on-offreflection pattern of the IRS may be expressed as in Equation 5 belowfrom Equation 3 above. On the other hand, in Equation 5, a noise part(that is, N_(u)) of Y_(u) may be omitted for concise expression.

$\begin{matrix}{\text{Y}_{u} = \sqrt{\rho}\left( {\text{U}_{M}\left( \varphi_{u} \right)\beta_{u}1_{K}^{T} + \text{u}_{M}\left( \upsilon_{f} \right)\alpha_{u}^{T}\text{U}_{N}^{H}\left( \xi_{u} \right)\text{W}} \right)} \\{= \sqrt{\rho}\left( {\text{U}_{M}\left( \varphi_{u} \right)\beta_{u}1_{K}^{T} + \text{u}_{M}\left( \upsilon_{f} \right)\alpha_{u}^{T}\text{U}_{K}^{H}\left( \xi_{u} \right)} \right)}\end{matrix}$

In Equation 5, U_(P)(ϑ) may denote an antenna steering matrix and may bedefined as U_(P)(ϑ) = [u_(P) (ϑ₁),···, u_(P)(ϑ_(Q))] with respect to anormalized angle set such as ϑ = [ϑ₁,···,ϑ_(Q)]^(T) . A manifold of alinear array antenna in the last line of Equation 5 may be maintainedwithout change using the on-off reflection pattern of the IRS. A columnvector space of Y_(u) may be generated using spatial antenna steeringvectors composed of φ_(u) and ψ_(ƒ). A row vector space of Y_(u) may begenerated using a vector in which all elements are 1 and an antennasteering vector of ξ_(u) obtained in a time domain.

First Operation-estimation of Ψ_(ƒ)

FIG. 5 is a flowchart illustrating the first operation of the method ofestimating a channel.

Referring to FIG. 5 , in order to use a temporal characteristic inoperation S401 of estimating ψ_(ƒ), the base station may suppress achannel component between the base station and the terminal. WhenEquation 5 is projected onto an orthogonal complement of a vector inwhich all elements are 1, the base station may express Equation 5 asEquation 6 below (S501).

$\text{Y}_{u}{\prod_{1_{K}}^{\bot}{= \sqrt{\rho}\text{u}_{M}\left( \upsilon_{f} \right)\alpha_{u}^{T}\text{U}_{K}^{H}\left( \xi_{u} \right){\prod_{1_{K}}^{\bot}\mspace{6mu}}}}$

In Equation 6,

$\prod_{\text{A}}^{\bot}\mspace{6mu}$

may be a projection matrix onto an orthogonal complement of a spacegenerated by a column vector of a matrix A and may be expressed as

${\prod_{\text{A}}^{\bot}{\triangleq \text{I}\text{−}\text{AA}^{\dagger}}}.$

. A sample covariance matrix for decomposing a signal subspace inEquation 6 may be calculated as in Equation 7 below (S502).

$\text{Y}_{u}{\prod_{1_{K}}^{\bot}\text{Y}_{u}^{H}} = \rho\left\| {\alpha_{u}^{T}\text{U}_{K}^{H}\left( \xi_{u} \right){\prod\begin{matrix}\bot \\1_{K}\end{matrix}}} \right\|\begin{matrix}2 \\2\end{matrix}\text{u}_{M}\left( \upsilon_{f} \right)\text{u}_{M}^{H}\left( \upsilon_{f} \right)$

In the covariance matrix of Equation 7, an eigenvector of a signalcomponent may correspond to an antenna steering vector u_(M) (ψ_(ƒ)) inψ_(ƒ). Therefore, in order to estimate an angle with high resolution,the base station may estimate ψ_(ƒ) using a root-MUSIC algorithm whichis a subspace-based technique that has been used in the past (S503). Thebase station may use a semi-definite programming (SDP) algorithm as wellas subspace-based algorithm (e.g., the root-MUSIC algorithm) to estimateψ_(ƒ).

Since a channel parameter ψ_(ƒ) between the base station and IRS iscommon to all terminals in a multi-user scenario, signals received fromthe U terminals may be commonly used to estimate ψ_(ƒ). Therefore, thesample covariance matrix may be calculated as in Equation 8 below.

$\sum\limits_{u = 1}^{U}{\text{Y}_{u}\text{Π}_{1_{K}}^{\bot}\text{Y}_{u}^{H} = \text{ρ}\left( {\sum\limits_{u = 1}^{U}\left\| {\alpha_{u}^{T}\text{U}_{K}^{H}\left( \xi_{u} \right)\text{Π}_{1_{K}}^{\bot}} \right\|_{2}^{2}} \right) \times \text{u}_{M}\left( \upsilon_{f} \right)\text{u}_{M}^{H}\left( \upsilon_{f} \right)}$

Since the largest eigenvalue in Equation 8 is larger than the largesteigenvalue in Equation 7, the base station may better separate a signalsubspace and a noise subspace. In addition, since either the SDP-basedalgorithm or the root-MUSIC algorithm is used, the method of estimatingψ_(ƒ) can be expanded to the case of a multi-path channel.

Second Operation-Estimation of ξu and Φ_(u)

FIG. 6 is a flowchart illustrating the second operation of the method ofestimating a channel.

Referring to FIG. 6 , in operation S402 of estimating ξ_(u) in thesecond operation after the estimation in the first operation, the basestation may project a space generated by the column vector of Y_(u) ontoa spatial antenna steering vector u_(M)(ψ _(ƒ)) (S601). ψ _(ƒ) maydenote an estimated value of ψ_(ƒ). A projected signal may be calculatedas in Equation 9 below.

$\begin{array}{l}{\text{Y}_{u}^{H}\text{u}_{M}\left( {\hat{\upsilon}}_{f} \right) = :{\overset{\rightarrow}{y}}_{u} = \left\lbrack {{\overset{\rightarrow}{y}}_{1,u},\cdots,{\overset{\rightarrow}{y}}_{K,u}} \right\rbrack^{T}} \\{= \sqrt{\text{ρ}}\underset{= :\text{U}_{K}{({\overset{\rightarrow}{\xi}}_{u})}}{\underset{︸}{\left\lbrack {1_{K}\mspace{6mu}\text{U}_{K}\left( \xi_{u} \right)} \right\rbrack}}\mspace{6mu}\underset{= :{\overset{\rightarrow}{\alpha}}_{u}}{\underset{︸}{\left\lbrack \begin{array}{l}{\left( {\text{U}_{M}\left( \varphi_{u} \right)\beta_{u}} \right)^{H}\text{u}_{M}\left( {\hat{\upsilon}}_{f} \right)} \\{\alpha_{u}^{*}\text{u}_{M}^{H}\left( \upsilon_{f} \right)\text{u}_{M}\left( {\hat{\upsilon}}_{f} \right)}\end{array} \right\rbrack}}}\end{array}$

In Equation 9, the base station may express the projected signal as afunction of α _(u) and

${\overset{\rightarrow}{\xi}}_{u}: = \left\lbrack {\xi_{0,u},\xi_{u}^{T}} \right\rbrack^{T}$

Since 1_(K) corresponds to an antenna steering vector corresponding toan angle of departure of 0, ξ_(0,u) may be expressed as ξ_(0,u) = 0.Since the base station considers additive white noise in Equation 3, anegative log likelihood with respect to

$\left( {{\overset{\rightarrow}{\xi}}_{u},\overset{\rightarrow}{\alpha_{u}}} \right)$

may be calculated as in Equation 10 below (S602).

$- \mspace{6mu}\ln p\left( {{\overset{\rightarrow}{y}}_{u};{\overset{\rightarrow}{\xi}}_{u},{\overset{\rightarrow}{\alpha}}_{u}} \right) \propto \left\| {{\overset{\rightarrow}{y}}_{u} - \text{U}_{K}\left( {\overset{\rightarrow}{\xi}}_{u} \right){\overset{\rightarrow}{\alpha}}_{u}} \right\|_{2}^{2}$

Since ξ _(u) and an unknown parameter α _(u) are combined in Equation10, it may be difficult for the base station to directly minimize thenegative log likelihood. Therefore, in the present example embodiment,the base station may obtain an optimal α _(u) and then may express thelikelihood as a function of only ξ _(u). When ξ _(u) is fixed, the basestation may obtain the optimal

${\overset{\rightarrow}{\alpha}}_{u}\mspace{6mu}\text{as}\mspace{6mu}{\hat{\overset{\rightarrow}{\alpha}}}_{u} = \left( {1/\sqrt{\rho}} \right)\text{U}_{K}^{\dagger}\left( {\overset{\rightarrow}{\xi}}_{u} \right){\overset{\rightarrow}{y}}_{u}$

using a least-squares method. When α _(u) is substituted into thenegative log likelihood of Equation 10, the base station may express

$\prod_{\text{U}_{K}{({\overset{\rightarrow}{\xi}}_{u})}}^{\bot}{= \text{I}_{K} -}$

$\text{U}_{K}\left( {\overset{\rightarrow}{\xi}}_{u} \right)\text{U}_{K}\left( {\overset{\rightarrow}{\xi}}_{u} \right)^{\dagger}\mspace{6mu}\text{as}\underset{{\overset{\rightarrow}{\xi}}_{u}}{\text{min}}\left\| {\text{Π}_{\text{U}_{K{({\overset{\rightarrow}{\xi}}_{u})}}}^{\bot}{\overset{\rightarrow}{y}}_{u}} \right\|_{2}^{2}$

through a maximum likelihood estimation method (S603).

An orthogonal complement of a space generated by a column vector of

$U_{k}\left( {\overset{\rightarrow}{\xi}}_{{}_{u}} \right)$

U_(K)(ξ _(u)) may be the same as a null space of (U_(K)(ξ_(u)))^(H).When it is defined that a basis of A ∈ ℂ^(K×(K-Lg-1)) generates a nullspace with respect to K ≥ L_(g) + 2, a maximum likelihood estimationequation may be re-expressed as

$\min\limits_{\text{A}}{\overset{\rightarrow}{y}}_{u}^{H}\text{A}\left( {\text{A}^{H}\text{A}} \right)^{- 1}\text{A}^{H}{\overset{\rightarrow}{y}}_{u}\mspace{6mu}.$

In the present example embodiment, since A the base station includes alinear array antenna structure, the matrix A may be expressed as apolynomial of

Α(z) = a₀z^(Lg + 1) + a₁z^(Lg) + ⋅ ⋅ ⋅ + a_(Lg + 1)

with respect to

z = e^(jπξ_(𝓁, u)), 𝓁 = 0, ⋅ ⋅ ⋅, L_(g)

and may be defined as in Equation 11 below.

$\text{A}^{H} = \begin{bmatrix}a_{L_{g} + 1} & \cdots & a_{1} & 1 & 0 & \cdots & 0 \\0 & a_{L_{g} + 1} & \cdots & a_{1} & 1 & \mspace{6mu} & \vdots \\ \vdots & \mspace{6mu} & \ddots & \mspace{6mu} & \ddots & \ddots & 0 \\0 & \cdots & 0 & a_{L_{g} + 1} & \cdots & a_{1} & 1\end{bmatrix}$

In Equation 11, the matrix A may satisfy a relationship of

$\left( \left\lbrack \text{A} \right\rbrack_{:,i} \right)^{H}\left\lbrack {\text{U}_{k}\left( {\overset{\rightarrow}{\xi}u} \right)} \right\rbrack:,\mathcal{l} = e^{j\pi\xi_{\mathcal{l},u}{({i - 1})}}\text{Α}\left( e^{j\pi\xi_{\mathcal{l},u}} \right) = 0$

and thus may satisfy

$\text{A}^{H}\text{U}_{K}\left( {\overset{\rightarrow}{\xi}}_{u} \right) = 0_{K - L_{g} - 1}0_{L_{g} + 1}^{T}\mspace{6mu}.$

Therefore, the base station may estimate ξ_(ℓ,u) by finding a root ofA(z). In addition, the base station may obtain a relationship of

$\text{A}^{H}{\overset{\rightarrow}{y}}_{u}a = {\overset{\rightarrow}{Y}}_{u}a$

using algebraic manipulation.

a = [a_(L_(g) + 1), ⋅ ⋅ ⋅, a₁, 1]^(T)

may denote a vector in which coefficients of (z) are accumulated, andY_(u) may be calculated as in Equation 12 below.

${\overset{\rightarrow}{\text{Y}}}_{u} = \begin{bmatrix}{\overset{\rightarrow}{y}}_{1,u} & & \cdots & {\overset{\rightarrow}{y}}_{L_{g} + 2,u} \\{\overset{\rightarrow}{y}}_{2,u} & & \cdots & {\overset{\rightarrow}{y}}_{L_{g} + 3,u} \\ \vdots & & & \vdots \\{\overset{\rightarrow}{y}}_{K - L_{g} - 1,u} & & \cdots & {\overset{\rightarrow}{y}}_{K,u}\end{bmatrix}$

The base station may redefine the maximum likelihood estimation methodas in

$\min\limits_{\text{a}\mspace{6mu}\text{s}\text{.t}\text{.}{\|\text{a}\|}_{2} = 1}\text{a}^{H}{\overset{\rightarrow}{\text{Y}}}_{u}^{H}\left( {\text{A}^{H}\text{A}} \right)^{- 1}{\overset{\rightarrow}{\text{Y}}}_{u}\text{a,}$

but a cost function involving complex operations such as an inversematrix operation cannot be solved analytically. Therefore, the basestation can solve maximum likelihood estimation for ξu through aniterative method. When a^((i)) is given in an i-th iteration, the basestation may calculate an inverse matrix of a Gram matrix such as(A^((i)H)A^((i)))⁻¹. a^((i+1)) may be calculated through a quadraticminimization problem as in Equation 13 below.

$\text{a}^{({i + 1})} = \mspace{6mu}\underset{\text{a}\mspace{6mu}\text{s}\text{.t}\text{.}{\|\text{a}\|}_{2} = 1}{\arg\min}\text{a}^{H}{\overset{\rightarrow}{\text{Y}}}_{u}^{H}\left( {\text{A}^{{(i)}H}\text{A}^{(i)}} \right)^{- 1}{\overset{\rightarrow}{\text{Y}}}_{u}\text{a}$

In Equation 13, a^((i+1)) may be an eigenvector corresponding to thesmallest eigenvalue of

${\overset{\rightarrow}{\text{Y}}}_{u}^{H}\left( {\text{A}^{{(i)}H}\text{A}^{(i)}} \right)^{- 1}{\overset{\rightarrow}{\text{Y}}}_{u}.$

When a^((i+1)) converges through an iteration, the base station mayestimate

${\overset{\rightarrow}{\xi}}_{u} = \left\lbrack {\xi_{0,u},\xi_{u}^{T}} \right\rbrack^{T}$

through a root of a polynomial A(z) (S604). The above-described methodmay be different from an existing iterative maximum likelihood method inthat ξ_(0,u) is known in advance. When the root of the polynomial A(z)(that is, ξ₀,_(u)) is known, since the number of parameters to beestimated may be reduced, and Y _(u)a may be substituted with Y_(u)[a]2:_(Lg+2) of which an order is reduced, the base station mayarrange an equation as in Equation 14 below.

${\overset{\smile}{\text{Y}}}_{u} = \left\lbrack {\overset{\rightarrow}{\text{Y}}}_{u} \right\rbrack_{:,2:L_{g} + 2} - \left\lbrack {\overset{\rightarrow}{\text{Y}}}_{u} \right\rbrack_{:,1}e^{j\pi\xi_{0,u}}\text{u}_{L_{g} + 1}^{T}\left( \xi_{0,u} \right)$

In Equation 14, a coefficient may be

a_(L_(g) + 1) = −e^(jπξ_(0, u))u_(L_(g) + 1)^(T)(ξ_(0, u))[a]_(2 : L_(g) + 2).

Since the base station may express Equation 13 as

$\min\limits_{{\lbrack\text{a}\rbrack}_{2:\text{Lg} + 2\mspace{6mu}\text{s}\text{.t}\text{.}\mspace{6mu}{\|{\lbrack\text{a}\rbrack}_{2:\text{Lg} + 2}\|}_{2} = 1}}\left( \left\lbrack \text{a} \right\rbrack_{2:\text{L}_{\text{g}} + 2} \right)^{H}{\overset{\smile}{\text{Y}}}_{u}^{H}\left( {\text{A}^{{(i)}H}\text{A}^{(i)}} \right)^{- 1}{\overset{\smile}{\text{Y}}}_{u}\left\lbrack \text{a} \right\rbrack_{2:\text{L}_{\text{g}} + 2}$

through Equation 14, it is possible to reduce computational complexity.

In operation S403 of estimating φ_(u) through a temporal characteristicof Y_(u), the base station may project a subspace generated by the rowvector of Y_(u) onto an array response vector, in which all elements are1, to express Y_(u)1_(K) as in Equation 15 below.

$\text{Y}_{u}1_{K} = \sqrt{\rho}\begin{bmatrix}{\text{U}_{M}\left( \varphi_{u} \right)} & {\text{u}_{M}\left( \upsilon_{f} \right)}\end{bmatrix}\mspace{6mu}\begin{bmatrix}{K\beta_{u}} \\{\alpha_{u}^{T}\text{U}_{K}^{H}\left( \xi_{u} \right)1_{K}}\end{bmatrix}$

Since Equation 15 and Equation 9 are very similar to each other, thebase station may estimate φ_(u) using the same iterative maximumlikelihood estimation method as in the estimation of (S605). The basestation can reduce computational complexity by applying Equation 14 asin the case of estimating ξ_(u) and ξ _(u) using ψ _(ƒ) estimated in thefirst operation of estimating a channel. ξu may denote an estimatedvalue of ξ_(u) , and φ _(u) may denote an estimated value of φ_(u).

Path Gain and Estimation of Α_(u) and β_(u)

After the base station estimates all parameters related to angles on apath, in order to estimate a path gain, the base station may transformEquation 5 into Equation 16 below to formulate a linear estimationproblem.

$\text{vec}\left( \text{Y}_{u} \right) = \underset{= :\text{Θ}{({\upsilon_{f},\xi_{u},\varphi_{u}})} \in {\mathbb{C}}^{MK \times {({L_{g} + L_{h}})}}}{\underset{︸}{\sqrt{\rho}\begin{bmatrix}{\text{U}_{K}^{*}\left( \xi_{u} \right) \otimes \text{u}_{M}\left( \upsilon_{f} \right)} & {1_{K} \otimes \text{U}_{M}\left( \varphi_{u} \right)}\end{bmatrix}\mspace{6mu}}}\begin{bmatrix}\alpha_{u} \\\beta_{u}\end{bmatrix}$

In Equation 16, vec(Y_(u)) may be in the form of a vector in which thecolumn vector of Y_(u) is accumulated. Therefore, the base station maylinearly estimate path gains α_(u) and β_(u) using

Θ(ψ_(f), ξ_(u), φ_(u))

which is estimated in advance.

Expandability to Planar Array Antenna

The above-described method of estimating a channel may be expanded froma linear array antenna to a planar array antenna by changing areflection pattern of an IRS. A planar array antenna in which an IRS hasN_(v) rows and N_(h) columns and includes a total of N reflectors may betaken into account. An azimuth angle and an elevation angle of an ℓ-thpath may be expressed as

ξ̃_(𝓁, u)^((h)) ∈ (0, π) and ξ̃_(𝓁, u)^((v)) ∈ (0, π),

respectively. An antenna steering vector of the IRS may be expressed inthe form of a Kronecker product of two antenna steering vectors as inEquation 17 below.

u(ξ_(𝓁, u)^((h)), ξ_(𝓁, u)^((v))) = u_(N_(h))(ξ_(𝓁, u)^((h))) ⊗ u_(N_(v))(ξ_(𝓁, u)^((v)))

In Equation 17, parameters related to an angle may be defined as

ξ_(𝓁, u)^((h)) : =

cos (ξ̃_(𝓁, u)^((h)))sin (ξ̃_(𝓁, u)^((v))) and ξ_(𝓁, u)^((v)) :  = cos (ξ̃_(𝓁, u)^((v))).

Therefore, Equation 9 may be expressed again as follows.

$\begin{array}{l}{{\overset{\rightarrow}{y}}_{u} = \text{Y}_{u}^{H}\text{u}_{M}\left( {\hat{\psi}}_{f} \right)} \\{= \sqrt{\rho}\left\lbrack {1_{K}\quad\text{W}^{H}\text{U}\left( {\xi_{u}^{(h)},\xi_{u}^{(v)}} \right)} \right\rbrack\left\lbrack \begin{array}{l}{\text{h}_{u}^{H}\text{u}_{M}\left( {\hat{\psi}}_{f} \right)} \\{\alpha_{u}^{\ast}\text{u}_{M}^{H}\left( \psi_{f} \right)\text{u}_{M}\left( {\hat{\psi}}_{f} \right)}\end{array} \right\rbrack}\end{array}$

An antenna steering matrix may be defined as in Equation 19 below.

U(ξ_(u)^((h)), ξ_(u)^((v))) = [u(ξ_(1, u)^((h)), ξ_(1, u)^((v))), ⋯, u(ξ_(L_(g), u)^((h)), ξ_(L_(g), u)^((v)))]

In order to apply the above-described method of estimating a channel tothe planar array antenna, the base station may divide an on-offreflection pattern of the IRS into vertical and horizontal elements.Accordingly, the on-off reflection patterns used in vertical andhorizontal directions may be calculated according to Equation 20 below.

$\begin{array}{l}{\text{W}^{(v)} = \text{e}_{N_{h}}\left( n_{h} \right) \otimes \text{I}_{N_{v}} \in {\mathbb{R}}^{N \times N_{v}}} \\{\text{W}^{(h)} = \text{I}_{N_{h}} \otimes \text{e}_{N_{v}}\left( n_{v} \right) \in {\mathbb{R}}^{N \times N_{h}}}\end{array}$

e_(p) (p) may denote a p-th column vector of I_(p), W^((v)) may meanthat an n_(h)-th column element is changed to an on state, and W^((h))may mean that a n_(v)-th row element is changed to an on state. FromEquations 17 and 20, a signal vector reflected by the IRS may beexpressed as Equation 21 below.

$\begin{array}{l}{\left( \text{W}^{(v)} \right)^{T}\text{u}\left( {\xi_{\mathcal{l},u}^{(h)},\xi_{\mathcal{l},u}^{(v)}} \right) = e^{j\pi\xi_{\mathcal{l},u}^{(h)}{({n_{h} - 1})}}\text{u}_{N_{v}}\left( \xi_{\mathcal{l},u}^{(v)} \right)} \\{\left( \text{W}^{(h)} \right)^{T}\text{u}\left( {\xi_{\mathcal{l},u}^{(h)},\xi_{\mathcal{l},u}^{(v)}} \right) = e^{j\pi\xi_{\mathcal{l},u}^{(v)}{({n_{v} - 1})}}\text{u}_{N_{h}}\left( \xi_{\mathcal{l},u}^{(h)} \right)}\end{array}$

In order to improve channel estimation performance, the base station mayintroduce new variables K_(v) and K_(h) indicating the number ofreflection iterations in the vertical and horizontal directions. Areflection pattern repeated during a training period may be expressed asin Equation 22 below.

W = [1_(K_(v))^(T) ⊗ W^((v))  1_(K_(h))^(T) ⊗ W^((h))]

According to Equation 22, training overhead may be K = K_(v)N_(v) +K_(h)N_(h). A pilot signal reflected by W^((v)) may be expressed as inEquation 23 below.

$\begin{matrix}{{\overset{\rightarrow}{y}}^{(v)} = {\sum\limits_{i = 1}^{K_{v}}\left\lbrack {\overset{\rightarrow}{y}}_{u} \right\rbrack_{{({i - 1})}N_{v} + 1:iN_{v}}}} \\{= K_{v}\sqrt{\text{ρ}}\left\lbrack {1_{K}\quad\text{U}_{K_{v}}\left( \xi_{u}^{(v)} \right)} \right\rbrack\begin{bmatrix}{\text{h}_{u}^{H}\text{u}_{M}\left( {\hat{\psi}}_{f} \right)} \\{\text{D}_{n_{h}}^{(h)}\alpha_{u}^{\ast}\text{u}_{M}^{H}\left( \psi_{f} \right)\text{u}_{M}\left( {\hat{\psi}}_{f} \right)}\end{bmatrix}}\end{matrix}$

In Equation 23, it may be defined that

D_(n_(h))^((h)) = diag(e^(jπξ_(1, u)^((h))(n_(h) − 1)), ⋯, e^(jπξ_(L_(g), u)^((h))(n_(h) − 1))).

A pilot signal reflected by W^((h)) may be expressed as in Equation 24below.

$\begin{matrix}{{\overset{\rightarrow}{y}}^{(h)} = {\sum\limits_{i = 1}^{K_{h}}\left\lbrack {\overset{\rightarrow}{y}}_{u} \right\rbrack_{{({i - 1})}N_{h} + 1 + K_{v}N_{v}:iN_{h} + K_{v}N_{v}}}} \\{= K_{h}\sqrt{\text{ρ}}\left\lbrack {1_{K}\quad\text{U}_{K_{h}}\left( \xi_{u}^{(h)} \right)} \right\rbrack\begin{bmatrix}{\text{h}_{u}^{H}\text{u}_{M}\left( {\hat{\psi}}_{f} \right)} \\{\text{D}_{n_{v}}^{(v)}\alpha_{u}^{\ast}\text{u}_{M}^{H}\left( \psi_{f} \right)\text{u}_{M}\left( {\hat{\psi}}_{f} \right)}\end{bmatrix}}\end{matrix}$

In Equation 24, it may be defined that

D_(n_(v))^((v)) = diag(e^(jπξ_(1, u)^((v))(n_(v) − 1)), ⋯, e^(jπξ_(L_(g), u)^((v))(n_(v) − 1))).

Received signals of Equations 23 and 24 may have the same form as thatof Equation 9 which is a received signal in the linear array antenna.Therefore, the base station may individually apply an algorithm appliedto the linear array antenna to an azimuth angle and an elevation angle.

By using the fact that both W^((v)) and W^((h)) in Equation 20 usen_(v)-th and n_(h)-th reflection elements, the base station can furtherreduce training overhead in addition to a reflection element shared at atime max{K_(v), K_(h)} in W of Equation 22.

The operations of the method according to the exemplary embodiment ofthe present disclosure can be implemented as a computer readable programor code in a computer readable recording medium. The computer readablerecording medium may include all kinds of recording apparatus forstoring data which can be read by a computer system. Furthermore, thecomputer readable recording medium may store and execute programs orcodes which can be distributed in computer systems connected through anetwork and read through computers in a distributed manner.

The computer readable recording medium may include a hardware apparatuswhich is specifically configured to store and execute a program command,such as a ROM, RAM or flash memory. The program command may include notonly machine language codes created by a compiler, but also high-levellanguage codes which can be executed by a computer using an interpreter.

Although some aspects of the present disclosure have been described inthe context of the apparatus, the aspects may indicate the correspondingdescriptions according to the method, and the blocks or apparatus maycorrespond to the steps of the method or the features of the steps.Similarly, the aspects described in the context of the method may beexpressed as the features of the corresponding blocks or items or thecorresponding apparatus. Some or all of the steps of the method may beexecuted by (or using) a hardware apparatus such as a microprocessor, aprogrammable computer or an electronic circuit. In some embodiments, oneor more of the most important steps of the method may be executed bysuch an apparatus.

In some exemplary embodiments, a programmable logic device such as afield-programmable gate array may be used to perform some or all offunctions of the methods described herein. In some exemplaryembodiments, the field-programmable gate array may be operated with amicroprocessor to perform one of the methods described herein. Ingeneral, the methods are preferably performed by a certain hardwaredevice.

The description of the disclosure is merely exemplary in nature and,thus, variations that do not depart from the substance of the disclosureare intended to be within the scope of the disclosure. Such variationsare not to be regarded as a departure from the spirit and scope of thedisclosure. Thus, it will be understood by those of ordinary skill inthe art that various changes in form and details may be made withoutdeparting from the spirit and scope as defined by the following claims.

What is claimed is:
 1. A method of estimating a channel of a basestation in a communication system using an intelligent reflectingsurface, the method comprising: receiving a first signal through adirect path between a terminal and the base station from the terminaland a second signal through an indirect path through the intelligentreflecting surface from the terminal; estimating a first angle ofarrival of the second signal received from the intelligent reflectingsurface; estimating a second angle of arrival of a signal transmitted tothe intelligent reflecting surface by the terminal based on theestimated first angle of arrival; estimating a third angle of arrival ofthe first signal received from the terminal based on the estimated firstangle of arrival; and estimating path gains on the direct path and theindirect path based on the estimated first angle of arrival to theestimated third angle of arrival.
 2. The method of claim 1, wherein thereceiving of the first signal through the direct path between theterminal and the base station from the terminal and the second signalthrough the indirect path through the intelligent reflecting surfacefrom the terminal further includes, when a third signal in which thefirst signal and the second signal are added is received from theterminal, separating the first signal and the second signal from thethird signal.
 3. The method of claim 1, wherein: the first angle ofarrival is estimated based on a first algorithm; and the first algorithmincludes at least one of a root-multiple signal classification(root-MUSIC) algorithm and a semi-definite programming algorithm.
 4. Themethod of claim 1, wherein the second angle of arrival is estimated byiteratively applying an array response vector in which all elements are1 and a maximum likelihood estimation method in a time domain.
 5. Themethod of claim 1, wherein the third angle of arrival is estimated byiteratively applying a maximum likelihood estimation method.
 6. Themethod of claim 1, wherein the path gain on the direct path and the pathgain on the indirect path are estimated based on a linear estimationmethod using the estimated first angle of arrival to the estimated thirdangle of arrival.
 7. The method of claim 1, wherein an on-off reflectionpattern of the intelligent reflecting surface is varied according to atype of an antenna array included in the base station.
 8. The method ofclaim 7, wherein the on-off reflection pattern is determined based onthe number of reflection repetitions.
 9. The method of claim 8, wherein,when the base station includes a planar array antenna, the on-offreflection pattern includes a reflection element shared when the numberof reflection repetitions in a horizontal direction and the number ofreflection repetitions in a vertical direction are each maximum.
 10. Themethod of claim 1, wherein: the intelligent reflecting surface includesa plurality of dynamically adjustable reflectors; and a communicationchannel between the intelligent reflecting surface and the base stationis a channel in which one line-of-sight propagation path is present. 11.A base station in a communication system using an intelligent reflectingsurface, the base station comprising: a processor; a memory configuredto electronically communicate with the processor; and instructionsstored in the memory, wherein, when the instructions are executed by theprocessor, the instructions operate to cause the base station to:receive a first signal through a direct path between a terminal and thebase station from the terminal and a second signal through an indirectpath through the intelligent reflecting surface from the terminal;estimate a first angle of arrival of the second signal received from theintelligent reflecting surface; estimate a second angle of arrival of asignal transmitted to the intelligent reflecting surface by the terminalbased on the estimated first angle of arrival; estimate a third angle ofarrival of the first signal received from the terminal based on theestimated first angle of arrival; and estimate path gains on the directpath and the indirect path based on the estimated first angle of arrivalto the estimated third angle of arrival.
 12. The base station of claim11, wherein, when the first signal through the direct path between theterminal and the base station and the second signal through the indirectpath through the intelligent reflecting surface are received from theterminal, the instructions operate to cause the base station to, when athird signal in which the first signal and the second signal are addedis received from the terminal, separate the first signal and the thirdsignal from the third signal.
 13. The base station of claim 11, wherein:the instructions operate to cause the base station to estimate the firstangle of arrival based on a first algorithm; and the first algorithmincludes at least one of a root-multiple signal classification algorithmand a semi-definite programming algorithm.
 14. The base station of claim11, wherein the instructions operate to cause the base station toestimate the second angle of arrival by iteratively applying an arrayresponse vector in which all elements are 1 and a maximum likelihoodestimation method in a time domain.
 15. The base station of claim 11,wherein the instructions operate to cause the base station to estimatethe third angle of arrival by iteratively applying a maximum likelihoodestimation method.
 16. The base station of claim 11, wherein theinstructions operate to cause the base station to estimate the path gainon the direct path and the path gain on the indirect path based on alinear estimation method using the estimated first angle of arrival tothe estimated third angle of arrival.
 17. The base station of claim 11,wherein the instructions operate to cause the base station to vary anon-off reflection pattern of the intelligent reflecting surfaceaccording to a type of an antenna array included in the base station.18. The base station of claim 17, wherein the instructions operate tocause the base station to determine the on-off reflection pattern basedon the number of reflection repetitions.
 19. The base station of claim18, wherein, when the base station includes a planar array antenna, theinstructions operate to cause the on-off reflection pattern to include areflection element shared when the number of reflection repetitions in ahorizontal direction and the number of reflection repetitions in avertical direction are each maximum.